Topics in Estimation and Inference with Multivariate Missing Data

Abstract

This dissertation discusses statistical methodologies for complex missing data problems with a focus on multivariate and partially observed structures. Chapter 2 introduces a unified framework for handling multiple missing covariates and partially observed responses using inverse probability weighting, regression adjustment, and a multiply-robust procedure. Applications include the Cox model for survival analysis, missing responses, and binary treatment in causal inference, along with supporting identification and asymptotic theory. Chapter 3 focuses on modeling multivariate bounded discrete outcomes such as those from neuropsychological tests in dementia studies. We propose a flexible modeling strategy based on mixtures of experts and latent class models, extended to handle missing at random outcomes via a nested EM algorithm. The joint model also allows for imputation and clustering. Chapter 4 addresses nonmonotone missing data under missing not at random (MNAR) mechanisms, extending the work in Chapter 3. A tree graph is a directed acyclic graph on the missing patterns, and each one represents a MNAR mechanism. Combining this with the idea of a conjugate odds property, we are able to preserve distributional structure across missing patterns and construct relatively straightforward models for the full data distribution. Throughout the dissertation, we also highlight practical relevance using an Alzheimer's disease data set.